A two-dimensional computer model is developed to study the evolution of texture during the growth of layered mineral aggregates. The program computes the number, size and orientation (texture) of crystals forming the outer surface of the aggregate, as well as the evolution as a function of time. In particular, the analysis focuses on the influence of growth parameters such as the anisotropy of the growing crystal forms, the relative growth rate of the crystal faces, the nucleation density on the substrate surface, the flow direction of the mineralizing solution and the shape of the substrate. The simulation provides an explanation for the development of a preferential orientation in a polycrystalline material growing from randomly oriented nuclei. The calculated distribution of crystal orientations, and its evolution with time, is in agreement with textures observed in synthetic and natural polycrystalline aggregates.